In order to prompt warm up of an exhaust purification catalyst provided to an internal combustion engine, there is known to be a technology such that by switching, for each cylinder, between rich combustion where combustion is executed with an air fuel ratio set on a rich side in comparison to a theoretical air fuel ratio and a lean combustion where combustion is executed with an air fuel ratio set on a lean side in comparison to a theoretical air fuel ratio, unburned fuel introduced to an exhaust passage and oxygen are supplied to the exhaust purification catalyst for oxidization, and by the reaction heat of the oxidization, temperature of the exhaust purification catalyst is raised, and thereby a catalyst warming operation is executed.
In such a catalyst warming operation, in a case that the rich combustion and the lean combustion are executed at their appropriate ignition timing respectively, a torque difference that output torque of a rich cylinder where the rich combustion is executed becomes higher than output torque of a lean cylinder where the lean combustion is executed occurs. For suppressing vibration and noise caused by the torque difference, suggested is a control apparatus which reduces the output torque of the rich cylinder by executing spark retardation where the ignition timing of the rich cylinder is retarded in comparison to its optimum ignition timing, and thereby reducing the torque difference between the output torque of the rich cylinder and the output torque of the lean cylinder (for example, Patent Literature #1).